Volume 39, Issue 2
Accelerated Optimization with Orthogonality Constraints

Jonathan W. Siegel

J. Comp. Math., 39 (2021), pp. 207-226.

Published online: 2020-11

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  • Abstract

We develop a generalization of Nesterov's accelerated gradient descent method which is designed to deal with orthogonality constraints. To demonstrate the effectiveness of our method, we perform numerical experiments which demonstrate that the number of iterations scales with the square root of the condition number, and also compare with existing state-of-the-art quasi-Newton methods on the Stiefel manifold. Our experiments show that our method outperforms existing state-of-the-art quasi-Newton methods on some large, ill-conditioned problems.

  • Keywords

Riemannian optimization, Stiefel manifold, Accelerated gradient descent, Eigenvector problems, Electronic structure calculations.

  • AMS Subject Headings

65K05, 65N25, 90C30, 90C48

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

jus1949@psu.edu (Jonathan W. Siegel)

  • BibTex
  • RIS
  • TXT
@Article{JCM-39-207, author = {Siegel , Jonathan W. }, title = {Accelerated Optimization with Orthogonality Constraints}, journal = {Journal of Computational Mathematics}, year = {2020}, volume = {39}, number = {2}, pages = {207--226}, abstract = {

We develop a generalization of Nesterov's accelerated gradient descent method which is designed to deal with orthogonality constraints. To demonstrate the effectiveness of our method, we perform numerical experiments which demonstrate that the number of iterations scales with the square root of the condition number, and also compare with existing state-of-the-art quasi-Newton methods on the Stiefel manifold. Our experiments show that our method outperforms existing state-of-the-art quasi-Newton methods on some large, ill-conditioned problems.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1911-m2018-0242}, url = {http://global-sci.org/intro/article_detail/jcm/18372.html} }
TY - JOUR T1 - Accelerated Optimization with Orthogonality Constraints AU - Siegel , Jonathan W. JO - Journal of Computational Mathematics VL - 2 SP - 207 EP - 226 PY - 2020 DA - 2020/11 SN - 39 DO - http://doi.org/10.4208/jcm.1911-m2018-0242 UR - https://global-sci.org/intro/article_detail/jcm/18372.html KW - Riemannian optimization, Stiefel manifold, Accelerated gradient descent, Eigenvector problems, Electronic structure calculations. AB -

We develop a generalization of Nesterov's accelerated gradient descent method which is designed to deal with orthogonality constraints. To demonstrate the effectiveness of our method, we perform numerical experiments which demonstrate that the number of iterations scales with the square root of the condition number, and also compare with existing state-of-the-art quasi-Newton methods on the Stiefel manifold. Our experiments show that our method outperforms existing state-of-the-art quasi-Newton methods on some large, ill-conditioned problems.

Jonathan W. Siegel. (2020). Accelerated Optimization with Orthogonality Constraints. Journal of Computational Mathematics. 39 (2). 207-226. doi:10.4208/jcm.1911-m2018-0242
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